Internal problem ID [5969]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.1. Page 332
Problem number: 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-2 x \relax (t )+5 y \relax (t )\\ y^{\prime }\relax (t )&=-2 x \relax (t )+4 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 44
dsolve([diff(x(t),t)=-2*x(t)+5*y(t),diff(y(t),t)=-2*x(t)+4*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {{\mathrm e}^{t} \left (\cos \relax (t ) c_{1}-3 \cos \relax (t ) c_{2}-3 \sin \relax (t ) c_{1}-c_{2} \sin \relax (t )\right )}{2} \] \[ y \relax (t ) = {\mathrm e}^{t} \left (\cos \relax (t ) c_{2}+\sin \relax (t ) c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 51
DSolve[{x'[t]==-2*x[t]+5*y[t],y'[t]==-2*x[t]+4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (c_1 \cos (t)+(5 c_2-3 c_1) \sin (t)) \\ y(t)\to e^t (c_2 (3 \sin (t)+\cos (t))-2 c_1 \sin (t)) \\ \end{align*}